Exploratory Analysis to Survival data

Background

Exploratory analysis for a survival data. The outcome Variables are OS and Death. In this analysis, we wanna do four things:

• Data preprocessing
• Statistical descriptive analysis
• Univariable analysis
• Mutivariable analysis including LASSO

Step 1 - Data preprocessing

library("readxl")
data_used <- read_excel(params$excel_path)

for (j in colnames(data_used)) {
  data_used[,j] <- as.numeric(as.matrix(data_used[,j]))
}
for (k in 1:length(colnames(data_used))){
  colnames(data_used)[k] <- gsub("-", "_", colnames(data_used)[k])
  colnames(data_used)[k] <- gsub("\\...", "col", colnames(data_used)[k])
}

Step 2 - Statistical descriptive analysis

2.1 summary information about outcome variables

Data Frame Summary

outcome_data

Dimensions: 99 x 2
Duplicates: 2

No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Missing
1	OS [numeric]	Mean (sd) : 14.4 (8.4) min < med < max: 1.8 < 11.1 < 33 IQR (CV) : 13 (0.6)	97 distinct values		0 (0%)
2	Death [factor]	1. 0 2. 1	7 ( 7.1% ) 92 ( 92.9% )		0 (0%)

Generated by summarytools 0.9.6 (R version 4.0.3)
2020-11-11

2.2 summary information about covariate

Data Frame Summary

covariates_data

Dimensions: 99 x 100
Duplicates: 0

No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Valid	Missing
1	Recurrence [factor]	1. 0 2. 1	8 ( 8.1% ) 91 ( 91.9% )		99 (100%)	0 (0%)
2	RFS [numeric]	Mean (sd) : 4.9 (3.4) min < med < max: 1 < 3.9 < 19.2 IQR (CV) : 3.5 (0.7)	94 distinct values		99 (100%)	0 (0%)
3	Chemotherapy [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
4	Gender [factor]	1. 0 2. 1	32 ( 32.3% ) 67 ( 67.7% )		99 (100%)	0 (0%)
5	Age [factor]	1. 0 2. 1	20 ( 20.2% ) 79 ( 79.8% )		99 (100%)	0 (0%)
6	Symptom [factor]	1. 0 2. 1	16 ( 16.2% ) 83 ( 83.8% )		99 (100%)	0 (0%)
7	BMI [factor]	1. 0 2. 1	34 ( 34.3% ) 65 ( 65.7% )		99 (100%)	0 (0%)
8	Size [factor]	1. 0 2. 1	26 ( 26.3% ) 73 ( 73.7% )		99 (100%)	0 (0%)
9	Lymphnode [factor]	1. 0 2. 1	59 ( 59.6% ) 40 ( 40.4% )		99 (100%)	0 (0%)
10	TBIL [factor]	1. 0 2. 1	29 ( 29.3% ) 70 ( 70.7% )		99 (100%)	0 (0%)
11	ALT [factor]	1. 0 2. 1	23 ( 23.2% ) 76 ( 76.8% )		99 (100%)	0 (0%)
12	GGT [factor]	1. 0 2. 1	23 ( 23.2% ) 76 ( 76.8% )		99 (100%)	0 (0%)
13	CA199 [factor]	1. 0 2. 1	37 ( 37.4% ) 62 ( 62.6% )		99 (100%)	0 (0%)
14	CEA [factor]	1. 0 2. 1	34 ( 34.3% ) 65 ( 65.7% )		99 (100%)	0 (0%)
15	Vascularinvasion [factor]	1. 0 2. 1	82 ( 82.8% ) 17 ( 17.2% )		99 (100%)	0 (0%)
16	filter_$ [numeric]	1 distinct value	1 : 99 ( 100.0% )		99 (100%)	0 (0%)
17	miR_1_rank [factor]	1. 0 2. 1	48 ( 48.5% ) 51 ( 51.5% )		99 (100%)	0 (0%)
18	miR_1 [numeric]	Mean (sd) : 4.3 (2.3) min < med < max: 0.4 < 4.8 < 8.8 IQR (CV) : 4.2 (0.5)	42 distinct values		99 (100%)	0 (0%)
19	miR_2_rank [factor]	1. 0 2. 1	57 ( 57.6% ) 42 ( 42.4% )		99 (100%)	0 (0%)
20	miR_2 [numeric]	Mean (sd) : 3.6 (2.4) min < med < max: 0.4 < 2.8 < 9.2 IQR (CV) : 3.9 (0.7)	42 distinct values		99 (100%)	0 (0%)
21	miR_3_rank [factor]	1. 0 2. 1	45 ( 45.5% ) 54 ( 54.5% )		99 (100%)	0 (0%)
22	miR_3 [numeric]	Mean (sd) : 4 (2.1) min < med < max: 0.4 < 4.4 < 8.6 IQR (CV) : 2.7 (0.5)	37 distinct values		99 (100%)	0 (0%)
23	miR_4_rank [factor]	1. 0 2. 1	54 ( 54.5% ) 45 ( 45.5% )		99 (100%)	0 (0%)
24	miR_4 [numeric]	Mean (sd) : 4 (2.2) min < med < max: 0.4 < 4 < 9.2 IQR (CV) : 3.1 (0.5)	38 distinct values		99 (100%)	0 (0%)
25	miR_5_rank [factor]	1. 0 2. 1	52 ( 52.5% ) 47 ( 47.5% )		99 (100%)	0 (0%)
26	col28 [numeric]	Mean (sd) : -4.2 (3.7) min < med < max: -11 < -3.4 < 1.4 IQR (CV) : 6.5 (-0.9)	51 distinct values		99 (100%)	0 (0%)
27	miR_5 [numeric]	Mean (sd) : 0.8 (3.7) min < med < max: -6 < 1.6 < 6.4 IQR (CV) : 6.5 (4.8)	51 distinct values		99 (100%)	0 (0%)
28	miR_6_rank [factor]	1. 0 2. 1	52 ( 52.5% ) 47 ( 47.5% )		99 (100%)	0 (0%)
29	miR_6 [numeric]	Mean (sd) : 0.7 (3.5) min < med < max: -6.8 < 1.8 < 6.2 IQR (CV) : 6.4 (4.7)	45 distinct values		99 (100%)	0 (0%)
30	miR_7_rank [factor]	1. 0 2. 1	53 ( 53.5% ) 46 ( 46.5% )		99 (100%)	0 (0%)
31	miR_7 [numeric]	Mean (sd) : 3.5 (2.5) min < med < max: -0.9 < 3.7 < 8 IQR (CV) : 4 (0.7)	99 distinct values		99 (100%)	0 (0%)
32	miR_8_rank [factor]	1. 0 2. 1	43 ( 43.4% ) 56 ( 56.6% )		99 (100%)	0 (0%)
33	miR_8 [numeric]	Mean (sd) : 3.9 (2.5) min < med < max: -0.7 < 4 < 8.3 IQR (CV) : 3.7 (0.6)	99 distinct values		99 (100%)	0 (0%)
34	miR_9_rank [factor]	1. 0 2. 1	57 ( 57.6% ) 42 ( 42.4% )		99 (100%)	0 (0%)
35	col37 [numeric]	Mean (sd) : -1 (2.3) min < med < max: -4.7 < -1.4 < 3.8 IQR (CV) : 3.7 (-2.4)	99 distinct values		99 (100%)	0 (0%)
36	miR_9 [numeric]	Mean (sd) : 4 (2.3) min < med < max: 0.3 < 3.6 < 8.8 IQR (CV) : 3.7 (0.6)	99 distinct values		99 (100%)	0 (0%)
37	miR_10_rank [factor]	1. 0 2. 1	46 ( 46.5% ) 53 ( 53.5% )		99 (100%)	0 (0%)
38	miR_10 [numeric]	Mean (sd) : -4 (2) min < med < max: -7.7 < -3.9 < -1 IQR (CV) : 3.2 (-0.5)	99 distinct values		99 (100%)	0 (0%)
39	miR_11_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
40	miR_11 [numeric]	Mean (sd) : 3.2 (2.2) min < med < max: -0.8 < 3.1 < 7 IQR (CV) : 3.6 (0.7)	99 distinct values		99 (100%)	0 (0%)
41	miR_12_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
42	miR_12 [numeric]	Mean (sd) : 4.4 (2.1) min < med < max: 0.9 < 4.4 < 7.7 IQR (CV) : 3.6 (0.5)	99 distinct values		99 (100%)	0 (0%)
43	miR_13_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
44	miR_13 [numeric]	Mean (sd) : 2.8 (2.9) min < med < max: -2.2 < 2.2 < 7.7 IQR (CV) : 5.2 (1)	99 distinct values		99 (100%)	0 (0%)
45	miR_14_rank [factor]	1. 0 2. 1	54 ( 54.5% ) 45 ( 45.5% )		99 (100%)	0 (0%)
46	miR_14 [numeric]	Mean (sd) : 4 (2.5) min < med < max: -0.5 < 4 < 8.4 IQR (CV) : 4 (0.6)	99 distinct values		99 (100%)	0 (0%)
47	miR_15_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
48	miR_15 [numeric]	Mean (sd) : 4.1 (2.4) min < med < max: 0.4 < 4.2 < 7.7 IQR (CV) : 4.4 (0.6)	99 distinct values		99 (100%)	0 (0%)
49	miR_16_rank [factor]	1. 0 2. 1	52 ( 52.5% ) 47 ( 47.5% )		99 (100%)	0 (0%)
50	miR_16 [numeric]	Mean (sd) : 3.6 (2.9) min < med < max: -1 < 3.7 < 8.8 IQR (CV) : 4.8 (0.8)	99 distinct values		99 (100%)	0 (0%)
51	miR_17_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
52	miR_17 [numeric]	Mean (sd) : 4.7 (2.2) min < med < max: 0.8 < 4.8 < 8 IQR (CV) : 3.6 (0.5)	99 distinct values		99 (100%)	0 (0%)
53	miR_18_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
54	miR_18 [numeric]	Mean (sd) : 3 (2.8) min < med < max: -1.6 < 2.4 < 8 IQR (CV) : 4.6 (0.9)	99 distinct values		99 (100%)	0 (0%)
55	miR_19_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
56	miR_19 [numeric]	Mean (sd) : 3.4 (2.8) min < med < max: -1.6 < 3.2 < 8.8 IQR (CV) : 4.3 (0.8)	99 distinct values		99 (100%)	0 (0%)
57	miR_20_rank [factor]	1. 0 2. 1	52 ( 52.5% ) 47 ( 47.5% )		99 (100%)	0 (0%)
58	miR_20 [numeric]	Mean (sd) : 2.4 (3.2) min < med < max: -2.9 < 2.1 < 7.7 IQR (CV) : 5.2 (1.4)	99 distinct values		99 (100%)	0 (0%)
59	miR_21_rank [factor]	1. 0 2. 1	45 ( 45.5% ) 54 ( 54.5% )		99 (100%)	0 (0%)
60	miR_21 [numeric]	Mean (sd) : 2.4 (3.2) min < med < max: -3.6 < 2.6 < 7.2 IQR (CV) : 5.4 (1.3)	99 distinct values		99 (100%)	0 (0%)
61	miR_22_rank [factor]	1. 0 2. 1	45 ( 45.5% ) 54 ( 54.5% )		99 (100%)	0 (0%)
62	miR_22 [numeric]	Mean (sd) : 2 (2.3) min < med < max: -2.4 < 2.4 < 5.3 IQR (CV) : 4.1 (1.2)	99 distinct values		99 (100%)	0 (0%)
63	miR_23_rank [factor]	1. 0 2. 1	46 ( 46.5% ) 53 ( 53.5% )		99 (100%)	0 (0%)
64	miR_23 [numeric]	Mean (sd) : -1.8 (3.3) min < med < max: -7.6 < -1.2 < 3.2 IQR (CV) : 5.5 (-1.8)	99 distinct values		99 (100%)	0 (0%)
65	miR_24_rank [factor]	1. 0 2. 1	55 ( 55.6% ) 44 ( 44.4% )		99 (100%)	0 (0%)
66	miR_24 [numeric]	Mean (sd) : -2.7 (3.2) min < med < max: -7.9 < -3.2 < 3.5 IQR (CV) : 5.1 (-1.2)	99 distinct values		99 (100%)	0 (0%)
67	miR_25_rank [factor]	1. 0 2. 1	54 ( 54.5% ) 45 ( 45.5% )		99 (100%)	0 (0%)
68	miR_25 [numeric]	Mean (sd) : 2.4 (3.3) min < med < max: -3.5 < 1.7 < 8.7 IQR (CV) : 4.8 (1.4)	99 distinct values		99 (100%)	0 (0%)
69	miR_26_rank [factor]	1. 0 2. 1	46 ( 46.5% ) 53 ( 53.5% )		99 (100%)	0 (0%)
70	miR_26 [numeric]	Mean (sd) : 1.3 (4.2) min < med < max: -6.5 < 2.2 < 7.6 IQR (CV) : 7.3 (3.2)	99 distinct values		99 (100%)	0 (0%)
71	miR_27_rank [factor]	1. 0 2. 1	48 ( 48.5% ) 51 ( 51.5% )		99 (100%)	0 (0%)
72	col74 [numeric]	Mean (sd) : 3.5 (3) min < med < max: -1.6 < 3.7 < 8.8 IQR (CV) : 5.2 (0.9)	99 distinct values		99 (100%)	0 (0%)
73	miR_27 [numeric]	Mean (sd) : -0.5 (3) min < med < max: -5.6 < -0.3 < 4.8 IQR (CV) : 5.2 (-6.2)	99 distinct values		99 (100%)	0 (0%)
74	miR_28_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
75	miR_28 [numeric]	Mean (sd) : -0.2 (3.3) min < med < max: -5.9 < -0.3 < 5.7 IQR (CV) : 5.6 (-17.1)	99 distinct values		99 (100%)	0 (0%)
76	miR_29_rank [factor]	1. 0 2. 1	49 ( 49.5% ) 50 ( 50.5% )		99 (100%)	0 (0%)
77	miR_29 [numeric]	Mean (sd) : 1.7 (4.1) min < med < max: -4.7 < 1.8 < 8 IQR (CV) : 7.3 (2.3)	99 distinct values		99 (100%)	0 (0%)
78	miR_30_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
79	miR_30 [numeric]	Mean (sd) : -0.9 (2.5) min < med < max: -5.3 < -1 < 3.4 IQR (CV) : 4.3 (-2.7)	99 distinct values		99 (100%)	0 (0%)
80	miR_31_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
81	miR_31 [numeric]	Mean (sd) : 2.6 (2.9) min < med < max: -2.5 < 2.4 < 7.3 IQR (CV) : 4.8 (1.1)	99 distinct values		99 (100%)	0 (0%)
82	miR_32_rank [factor]	1. 0 2. 1	43 ( 43.4% ) 56 ( 56.6% )		99 (100%)	0 (0%)
83	miR_32 [numeric]	Mean (sd) : -2.3 (3.5) min < med < max: -8.3 < -1.8 < 3.3 IQR (CV) : 6.7 (-1.5)	99 distinct values		99 (100%)	0 (0%)
84	miR_33_rank [factor]	1. 0 2. 1	52 ( 52.5% ) 47 ( 47.5% )		99 (100%)	0 (0%)
85	miR_33 [numeric]	Mean (sd) : -0.5 (2.3) min < med < max: -4.5 < -0.6 < 3.6 IQR (CV) : 3.8 (-4.2)	99 distinct values		99 (100%)	0 (0%)
86	miR_34_rank [factor]	1. 0 2. 1	47 ( 47.5% ) 52 ( 52.5% )		99 (100%)	0 (0%)
87	miR_34 [numeric]	Mean (sd) : -2 (3) min < med < max: -7.5 < -2 < 3.7 IQR (CV) : 4.8 (-1.5)	99 distinct values		99 (100%)	0 (0%)
88	miR_35_rank [factor]	1. 0 2. 1	50 ( 50.5% ) 49 ( 49.5% )		99 (100%)	0 (0%)
89	miR_35 [numeric]	Mean (sd) : -1 (3.6) min < med < max: -6.4 < -0.7 < 4.8 IQR (CV) : 6.6 (-3.8)	99 distinct values		99 (100%)	0 (0%)
90	miR_36_rank [factor]	1. 0 2. 1	56 ( 56.6% ) 43 ( 43.4% )		99 (100%)	0 (0%)
91	miR_36 [numeric]	Mean (sd) : -0.8 (3) min < med < max: -5.6 < -1.1 < 4.8 IQR (CV) : 5.3 (-4)	99 distinct values		99 (100%)	0 (0%)
92	miR_37_rank [factor]	1. 0 2. 1	49 ( 49.5% ) 50 ( 50.5% )		99 (100%)	0 (0%)
93	miR_37 [numeric]	Mean (sd) : -2.3 (3.7) min < med < max: -8.5 < -3 < 4.8 IQR (CV) : 6.3 (-1.6)	99 distinct values		99 (100%)	0 (0%)
94	miR_38_rank [factor]	1. 0 2. 1	55 ( 55.6% ) 44 ( 44.4% )		99 (100%)	0 (0%)
95	miR_38 [numeric]	Mean (sd) : -1.3 (2.8) min < med < max: -5.6 < -1.7 < 3.7 IQR (CV) : 4.7 (-2.3)	99 distinct values		99 (100%)	0 (0%)
96	miR_39_rank [factor]	1. 0 2. 1	55 ( 55.6% ) 44 ( 44.4% )		99 (100%)	0 (0%)
97	miR_39 [numeric]	Mean (sd) : -1.3 (3.4) min < med < max: -6.5 < -1.5 < 4.4 IQR (CV) : 5.9 (-2.7)	99 distinct values		99 (100%)	0 (0%)
98	miR_40_rank [factor]	1. 0 2. 1	51 ( 51.5% ) 48 ( 48.5% )		99 (100%)	0 (0%)
99	col101 [numeric]	Mean (sd) : 4.3 (2.5) min < med < max: 0.6 < 4 < 8.7 IQR (CV) : 4.5 (0.6)	99 distinct values		99 (100%)	0 (0%)
100	miR_40 [numeric]	Mean (sd) : -0.7 (2.5) min < med < max: -4.4 < -1 < 3.7 IQR (CV) : 4.5 (-3.7)	99 distinct values		99 (100%)	0 (0%)

Generated by summarytools 0.9.6 (R version 4.0.3)
2020-11-11

2.3 The distribution of continus variables

2.4 The box plot of continus variables

2.5 The correlation heatmap plot of continus variables

2.6 The bar plot of cateogorical variables

Step 3 - Univariable analysis

3.1 Results of Univariable analysis for OS and Death

3.2 Significant variable in univariate analysis

 [1] "RFS"          "miR_1"        "miR_2"        "miR_3"        "miR_4"       
 [6] "col28"        "miR_5"        "miR_6"        "miR_24"       "miR_28"      
[11] "Chemotherapy" "Age"          "Lymphnode"    "TBIL"         "ALT"         
[16] "CEA"          "miR_1_rank"   "miR_2_rank"   "miR_3_rank"   "miR_6_rank"  
[21] "miR_24_rank" 

3.3 KM plot for categorical variables

3.4 box plot for continus variables

Step 4 - Mutivariable analysis

4.1 Stepwise for model selection when containing all significant variables in univiate analysis.

Call:
coxph(formula = Surv(OS, Death) ~ RFS + col28 + miR_6 + miR_28 + 
    Chemotherapy + Lymphnode + CEA, data = data_frame)

                  coef exp(coef) se(coef)      z        p
RFS           -0.89899   0.40698  0.12867 -6.987 2.82e-12
col28         -0.10500   0.90032  0.03628 -2.895 0.003797
miR_6         -0.21194   0.80901  0.04207 -5.038 4.71e-07
miR_28        -0.05771   0.94393  0.03713 -1.554 0.120192
Chemotherapy1  0.44283   1.55710  0.26161  1.693 0.090518
Lymphnode1     0.44097   1.55421  0.23912  1.844 0.065163
CEA1          -0.96779   0.37992  0.26365 -3.671 0.000242

Likelihood ratio test=170.3  on 7 df, p=< 2.2e-16
n= 99, number of events= 92 

4.2 LASSO

4.2.1 Variables selected by Lasso Cox using C-index metrics

 [1] "RFS"         "miR_1"       "col28"       "miR_5"       "miR_6"      
 [6] "miR_10"      "miR_11"      "miR_12"      "miR_13"      "miR_14"     
[11] "miR_15"      "miR_17"      "miR_18"      "miR_19"      "miR_28"     
[16] "miR_31"      "miR_33"      "miR_36"      "miR_37"      "col101"     
[21] "miR_40"      "Recurrence"  "Gender"      "Size"        "Lymphnode"  
[26] "GGT"         "CEA"         "miR_8_rank"  "miR_15_rank" "miR_20_rank"
[31] "miR_22_rank" "miR_23_rank" "miR_34_rank" "miR_35_rank" "miR_38_rank"
[36] "miR_39_rank"

4.2.2 Coefficient of Lasso Cox in optimal lambda

99 x 1 sparse Matrix of class "dgCMatrix"
                             1
RFS              -6.900427e-01
miR_1             1.017145e-02
miR_2             .           
miR_3             .           
miR_4             .           
col28            -7.373156e-02
miR_5            -5.849148e-17
miR_6            -2.361290e-01
miR_7             .           
miR_8             .           
col37             .           
miR_9             .           
miR_10           -1.367586e-02
miR_11           -7.218946e-03
miR_12           -1.554560e-02
miR_13            8.930393e-03
miR_14            7.257140e-04
miR_15            5.386218e-03
miR_16            .           
miR_17           -8.331654e-02
miR_18           -4.054314e-02
miR_19           -8.102817e-02
miR_20            .           
miR_21            .           
miR_22            .           
miR_23            .           
miR_24            .           
miR_25            .           
miR_26            .           
col74             .           
miR_27            .           
miR_28           -5.725081e-02
miR_29            .           
miR_30            .           
miR_31           -6.345782e-02
miR_32            .           
miR_33           -1.504876e-02
miR_34            .           
miR_35            .           
miR_36            6.305918e-02
miR_37            3.151431e-02
miR_38            .           
miR_39            .           
col101            2.815717e-03
miR_40            7.174788e-16
Recurrence       -1.117257e+00
Chemotherapy      .           
Gender            2.041213e-01
Age               .           
Symptom           .           
BMI               .           
Size              1.801825e-01
Lymphnode         1.785151e-01
TBIL              .           
ALT               .           
GGT              -1.318687e-01
CA199             .           
CEA              -7.631035e-01
Vascularinvasion  .           
miR_1_rank        .           
miR_2_rank        .           
miR_3_rank        .           
miR_4_rank        .           
miR_5_rank        .           
miR_6_rank        .           
miR_7_rank        .           
miR_8_rank       -3.303187e-02
miR_9_rank        .           
miR_10_rank       .           
miR_11_rank       .           
miR_12_rank       .           
miR_13_rank       .           
miR_14_rank       .           
miR_15_rank       4.386973e-03
miR_16_rank       .           
miR_17_rank       .           
miR_18_rank       .           
miR_19_rank       .           
miR_20_rank       2.811178e-03
miR_21_rank       .           
miR_22_rank       1.001493e-01
miR_23_rank      -3.764196e-01
miR_24_rank       .           
miR_25_rank       .           
miR_26_rank       .           
miR_27_rank       .           
miR_28_rank       .           
miR_29_rank       .           
miR_30_rank       .           
miR_31_rank       .           
miR_32_rank       .           
miR_33_rank       .           
miR_34_rank       1.052107e-01
miR_35_rank       1.150351e-02
miR_36_rank       .           
miR_37_rank       .           
miR_38_rank       3.635169e-01
miR_39_rank       6.389360e-02
miR_40_rank       .           

4.2.3 Coefficient change as L1 norm in Lasso Cox

4.2.4 Change of C-index